Brotzman was born on a farm in near Sterling, Colorado in Logan County to Priscella Ruth Kittle Smith (1895–1986) and Harry Brotzman (1895–1959). He was educated in Logan County schools. He married Louise L. Reed on April 9, 1944. He served in the United States Army as a first lieutenant with the Eighty-first Infantry Division in the South Pacific from 1945 to 1946.

Brotzman was elected as a Republican to the Eighty-eighth Congress (January 3, 1963 – January 3, 1965). He was an unsuccessful nominee in 1964 to the Eighty-ninth Congress. He was elected to the Ninetieth and to the three succeeding Congresses (January 3, 1967 – January 3, 1975). He was an unsuccessful candidate for reelection to the Ninety-fourth Congress in 1974.

Brotzman died of cancer Sept. 15 at the Fountains at Washington House, a nursing home in Alexandria. He lived in Alexandria.

Survivors include his wife, Gwendolyn Davis Brotzman of Alexandria, whom he married in 1996; two children from his first marriage, Kathleen "Kathy" Caldwell of Longmont, Colo., and Donald G. "Chip" Brotzman Jr. of Carbondale, Colo.; a stepson, Robert Higgins of Philippi, W.Va.; a brother; and six grandchildren.